# The width of a rectangle is 9 inches less than 4 times the length. If x represents the length, how do you write an algebraic expression in terms of x that represents the area of the rectangle?

Mar 20, 2016

Area$= 4 {x}^{2} - 9 x$

#### Explanation:

We will convert the variable to include $x$ afterwards

Breaking down the question into its component parts

Let width be $W$
Let length be $L$
Let area be $A$

The width of a rectangle $\to W$
is ->W=?
9 inches less than->W=?-9
4 times->W=(4xx?)-9
the length$\to W = \left(4 \times L\right) - 9$

If x represents length$\to W = \left(4 \times x\right) - 9$

Width$\to \textcolor{g r e e n}{W = 4 x - 9}$

Area is calculated by $\textcolor{g r e e n}{\text{width}}$ times $\textcolor{m a \ge n t a}{\text{length}}$.

In this case $A = \textcolor{g r e e n}{W} \textcolor{m a \ge n t a}{x}$

Substituting for width gives

$A = \textcolor{g r e e n}{\left(4 x - 9\right)} \textcolor{m a \ge n t a}{x}$

Multiplying out the bracket gives

$A = 4 {x}^{2} - 9 x$